Britain’s Prince Harry swept the Big Apple off its feet yesterday as he made a heartfelt visit to Ground Zero and chatted with wounded veterans at a city VA hospital.

The once-raucous royal showed off a serious and somber side that impressed the many New Yorkers he met.

“He was really concerned; he feels the pain of the victims,” said Monica Iken, 39, whose husband, Michael, died on 9/11, and who spoke to Harry at Ground Zero.

“He wanted to hear my story,” she said. “It was unbelievable he took the time to visit and make this his first stop. He said this is what he wanted to do; he wanted to visit the memorial.”

The royal visit began at about noon as the prince met with family members of people lost on 9/11 and with Port Authority officials.

After the PA showed the prince blueprints for the long-delayed World Trade Center redevelopment project, Harry caused an unintentionally embarrassing moment for the officials when he innocently asked: “Big question — when is this supposed to be finished?”

The officials cited the current planned finishing dates for the various projects, including the expected completion of the memorial, transit hub and new skyscraper by 2014.

Harry had a lighter moment when he went to the nearby Engine 10/Ladder 10 firehouse on Liberty Street, which lost six members on 9/11.

He was given patches and FDNY T-shirts as gifts from the firefighters and said “I’m one of the men now.”

The red-headed prince also joked with red-headed firefighter Kyle Rowe that he was glad to meet a “fellow ginger.”

Harry next visited the British Memorial Garden in Hanover Square, a memorial to the 67 UK citizens who died on Sept. 11. He was greeted by squealing young women as he planted a remembrance tree.

After that, he moved on to the Veterans Administration Hospital on East 23rd Street, where wounded Iraq veteran Paul Yarbrough demonstrated a new prosthetic hand.

He ended the day with a reception at the British Consulate. Guests represented a cross-section of New York, from Katie Couric to New York Jet football star Jerricho Cotchery.

Afterward, when asked about his big day in the Big Apple Harry said: “It was great.” With Post Wire Services